Modern Portfolio Theory (MPT), especially in the context of Capital Asset Pricing Model (CAPM) first developed by William Sharpe and John Linter, assumes that an investor maximizes his/her terminal wealth by investment portfolio decisions made today. In making investment portfolio decisions, an investor attempts to examine every possible investment opportunity to form an efficient portfolio frontier and picks the most efficient portfolio vector for maximizing an investment return. Since every prudent investor would do this, the most efficient portfolio that he or she picks would be the same for all, given risk-free lending and borrowing rates. Such an investment portfolio is known as market portfolio.
However, people differ in their risk preferences. Consequently, some investors might mix their investments in market portfolio with risk-free or less risky assets, while others might prefer to invest exclusively in the market portfolio with borrowed funds. Alternatively, people might hold a well-diversified mutual fund, which generally will result in a similar risk-return profile as that achievable by an individual portfolio, which combines market portfolio and risk-free assets under the CAPM theory.
However, determining how individual asset returns are generated under conditions of market uncertainty is not provided by MPT. This has not only been a crucial element missing from MPT, but is also an important consideration to all investment practitioners in real world trading, because each individual security return would eventually determine the expected returns and variance of every portfolio containing that security and, hence, will determine the shape of the efficient portfolio frontier under MPT.
The originally developed CAPM has very little to say about how each individual security return is generated. Various improvements to the original CAPM have been proposed, such as the Single Index CAPM and various other forms of Multi-Factor CAPMs (with or without various taxes, transaction costs, inflation rates, and the like). On the other hand, Arbitrage Pricing Theory (APT) by Steve Ross proposes that whatever results the CAPM may have produced must be a result of the investor arbitrage. As a result, Professor Ross starts out with the theory of a k-factor return generating function for each individual security; and assumes that every investor would be interested in making risk-free profits by forming an arbitrage investment portfolio utilizing his pre-specified return generating function of linearity for each individual security. According to Professor Ross' theory, the final pricing formula for capital asset prices would be similar to that of the CAPM.
Factors determining individual security returns are proprietary to every security analyst. Every portfolio manager has his/her own set of factors. Generally, what determines the security returns follows a return generating function in a form described in equation (1) below
                              R          i                =                              α            i                    +                                    ∑                              i                =                1                            k                        ⁢                                                  ⁢                                          β                ij                            ⁢                              F                j                                              +                      ɛ            i                                              (        1        )            where Ri is a rate of return on a security, i; Fj is an investment style economic factor, j, affecting all security returns; αi is a regression constant; βij is the sensitivity of the return on a security, i, with respect to a change in factor, j. Those j factors may include industry identifiers, the inflation rate, the unemployment rate, exchange rates, economic growth rates, interest rates, price-earnings, firm size, market to book value, and so forth.
Since an investment portfolio return is defined as
            R      p        =                  ∑                  i          =          1                n            ⁢                          ⁢                        X          i                ⁢                  R          i                      ,where Xi's are respectively a proportion in which an investment is made in a security, i, the expected return E and the standard deviation σ for a risky portfolio are respectively defined as
                                          E            ⁡                          [                              R                p                            ]                                =                                    ∑                              i                =                1                            n                        ⁢                                                  ⁢                                          X                i                            ⁢                              E                ⁡                                  [                                      R                    i                                    ]                                                                    ,        and                            (        2        )                                          σ          p          2                =                                            ∑                              i                =                1                            n                        ⁢                                                  ⁢                                          X                i                2                            ⁢                              σ                i                2                                              +                                    ∑                              i                =                1                            n                        ⁢                                                  ⁢                                                            ∑                                      j                    =                    1                                    n                                                  j                  ≠                  i                                            ⁢                                                          ⁢                                                X                  i                                ⁢                                  X                  j                                ⁢                                  σ                  ij                                                                                        (        3        )            
Techniques of maximizing the portfolio's expected return, E[Rp] and minimizing the portfolio's risk, σp2, have been well documented in many finance textbooks. However, the proposed techniques are often inadequate or even incomplete from most investors' point of view.
For example, the market portfolio under MPT exists only in theory. Since the market portfolio as suggested in MPT is only a theoretical construct, it is possible that efficient portfolios selected by sub-sampled stocks may outperform (or underperform) any available market benchmark index, which many investors use as a proxy for the market portfolio. Furthermore, properties of the probability distribution for security returns, as are given in equation (1), are not constant over time. To understand this, a great deal of theoretical research has been done in the area of MPT by utilizing various stochastic process models. However, there has been no definite conclusion as to how an individual portfolio should readjust itself to an optimum portfolio in a dynamic stochastic model. Consequently, it is quite difficult for an investor to plan ahead to maximize his terminal wealth when the probability distribution parameters change in the face of constantly changing investment environments in real time. In addition, as of the date when this application is filed, there has been no known computational facility currently available to individual investors through the Internet or other communication channels designed to show how an optimum portfolio should be formed or approached by taking into consideration all assumptions made in MPT.
Moreover, no known tool incorporating efficient portfolio modeling theories (e.g., CAPM) is currently available to investors through the Internet, or other communication channels, that is designed to provide many desirable features in helping investors to make their investment decisions with respect to portfolio management. Consequently, individual investors often have to rely on professional portfolio managers in making investment decisions using, among others, the above-mentioned market portfolio theories. These desirable decision-making features may include:                To show how one can pick a scenario portfolio, which may outperform a given market index by selecting stocks through (i) various stock screening features, (ii) back tests, and/or (iii) virtual trades;        To show how one can better manage his or her portfolios by recognizing the bid/ask spread, brokerage commissions, potential tax obligations, etc., in real time;        To show how one can attempt to re-balance his or her own portfolios by suggesting various criteria or preferences with a possible trading band;        To present a financial statement for each one of their investment portfolio accounts;        To show how a risk level rises or falls in real time, as he or she manages his or her own portfolios;        To execute and settle orders automatically in real time, especially those orders involving a basket of securities;        To show automatically how investors could allocate investment assets in real time; or        To provide various investment calculators for investment analysis purposes.        